Eunice was the mother of Timothy and a Jewish believer in Christ. Eunice was the daughter of Lois, and she was married to a Greek man. The brethren in Lystra and Iconium said good things about Timothy, and Paul decided to have Timothy accompany him. Paul circumcised Timothy, and together, they spread Christianity and the decrees of the apostles and the elders residing in Jerusalem.
In a letter to Timothy, Paul mentioned Eunice, Lois, and their strong faith.
I [Paul] remember your [Timothy's] sincere and unqualified faith [the surrendering of your entire self to God in Christ with confident trust in His power, wisdom and goodness, a faith] which first lived in [the heart of] your grandmother Lois and your mother Eunice, and I am confident that it is in you as well.— 2 Timothy 1:5 (AMP)
The Jewish heritage of Eunice and Lois is presumably how Timothy came to learn the Scriptures during childhood. In one of his letters, Paul told Timothy to keep in mind from whom he had learned and how he had known the Scriptures since childhood.
But as for you, continue in the things that you have learned and of which you are convinced [holding tightly to the truths], knowing from whom you learned them, and how from childhood you have known the sacred writings (Hebrew Scriptures) which are able to give you the wisdom that leads to salvation through faith which is in Christ Jesus [surrendering your entire self to Him and having absolute confidence in His wisdom, power and goodness].— 2 Timothy 3:14–3:15 (AMP)